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% polarization of partially polarized light

  1. Mar 14, 2009 #1
    1. Here's the question:

    The percent polarization P of a partially polarized beam of light is defined as

    P = [Imax - Imin]/[Imax + Imin] x 100

    where Imax and Imin are the max and min intensities that are obtained when the light
    passes through a polarizer that is slowly rotated. Such light can be considered as the
    sum of two unequal plane-polarized beams of intensities Imax and Imin perpindicular to
    eachother. Show that the light transmitted by a polarizer, whose axis makes an angle
    theta to the direction in which Imax is obtained, has intensity

    [1 + pcos(2theta)]/[1 + p]

    where p = P/100.

    2. Relevant equations

    I = I# x cos^2(theta) (I# is I naught, or initial intensity)

    3. I thought that the intensity would be at a maximum when theta=0 degrees, because
    cosine of 0 is 1, so the Intensity of the polarized light would be equal to the intensity
    of the light initially, but that doesn't seem to work out to something that resembles
    the answer. I also thought that maybe p=cos^2(theta), since it is the fractional
    percentage of the initial intensity. I also tried coming up with equations for Imax and
    Imin, but I wasn't sure whether or not they would have the same angles and
    intensities. Any help with this problem would be greatly appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: Mar 15, 2009
  2. jcsd
  3. Mar 15, 2009 #2

    berkeman

    User Avatar

    Staff: Mentor

    Remember that you should add the two contributions for the two orthogonal "sources". So write one equation for the intensity distribution of one source, and another for the intensity distribution of the orthogonal source, and then add them, under the constraint of the top equation for the percent variation between the two sources....

    Show us some of those equations, and I think you will be mostly there...
     
  4. Mar 15, 2009 #3
    okay, so here's what I have so far

    I (as a function of theta) = Imaxcos^2theta
    Imaxcos^2theta = Imax + Imin
    Imax(cos^2theta-1) = Imin
    Imax(cos2theta) = Imin

    am I on the right path?
     
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